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Tag: Analytic Hierarchy Process

A new version of of the AHP Excel template with some major updates is now available for download. Based on the work of Tomashevskii (2014, 2015), errors for the resulting priorities/weights are shown.

Calculated weights with error indication

In addition the overall dissonance (ordinal inconsistency) according to Sajid Siraj (2011) is indicated. The zip file for download also contains the updated manual, showing the calculations and references.

In this latest version of the template, the balanced scale was replaced by the generalized balanced scale (balanced-n), and the adaptive scale was added. The maximum number of iterations for the power method was increased from 12 to 20.

If you need inputs for more than 20 participants, please contact the author. A version for up to 225 participants is available.

I’m thankful to the program committee to have received the most innovative idea reward for the paper about AHP-OS.

Some interesting papers were presented, for example Cardinal and Ordinal Inconsistency in pairwise Comparison Matrices by Konrad Kulakowski, or Coherency: an Innovation to Test Data Quality and Reduced Comparisons in the ANP by Orrin Cooper, just to mention two.

I will update you with the link, once the conference proceedings are published.
The conference gave participants also an opportunity for many discussions and the exchange of ideas.

Please continue to support my effort, either with a donation, or a rating to my web posts, which will help me as a feedback to my work.

For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated. And don’t forget: Better to be approximately right than precisely wrong.

Klaus D. Goepel,

Singapore, July 2018

BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use.

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

I wish all of you a Happy and Prosperous New Year 2018!

From July 13th to 15th the International Symposium on the Analytic Hierarchy Process (ISAHP) for Decision Making takes place in Hong Kong. Poster submission is possible from Nov 1st, 2017 to Mar 15th, 2018 and individual paper submission from Nov 1st, 2017 to Mar 6th. Early registration deadline May 15th, 2018. More Information about the ISAHP 2018 can be found on their website.

After my last participation in 2013, I plan to attend the conference in July. If you want to meet me personally, feel free to contact me. I submitted an individual paper about the implementation of my AHP-OS software; it is a short version of my detailed working paper. In additon I will probably submit a short version of my paper Comparison of Judgment Scales of the Analytical Hierarchy Process – A New Approach. This paper was submitted to the International Journal of Information Technology and Decision Making in June 2017, and is under review since then. All attempts to contact the editors and to find out, why the review process takes so long, were unsuccessful.

My AHP-OS software has now reached nearly 6000 registrations since its implementation in 2014. It should be quite stable and without major bugs. Unfortunately, there is still a minor sporadic problem with the storage of pairwise comparisons. It appears in 1 out of 1000 projects that a set pairwise comparisons just disappears. I am still trying to find the reason, kindly contact me, when this happens to you, and let me know the circumstances (It seems to have something to do with the browser and stored session data).

Please continue to support my effort, either with a donation, or at least give a 1 (poor) to 5 (excellent) rating to my web posts, which will help me to get some feedback on my work.

For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated.

Klaus D. Goepel,

Singapore, Jan 2018

BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use.

Concepts, Methods and Tools to manage Business Performance

Dear Friends, dear Visitors,

Over the last three months I did a lot of under-the-hood changes and clean-up on the website to improve safety and user experience. As you may have noticed, the protocol is now https: the web traffic is encrypted using an SSL client certificate. After some tweaking the page performance could be improved significantly, loading time is nearly reduced by half. All pages, including my AHP-OS online software and the diversity calculator, were made mobile friendly, though I don’t recommend to use AHP-OS on a small mobile phone screen.

In addition some new features were added to the AHP-OS online software:

I also wrote a paper about the AHP software implementation, where you can find a description of the structure and all mathematical formulas and references. Please make a reference to this paper, when you use the software in your work to be published.

Kindly support my effort, either with a donation, or at least give a 1 (poor) to 5 (excellent) rating to my web posts, which will help me to get some feedback on my work.

For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated.

Klaus D. Goepel,

Singapore, September 2017

BPMSG stands for Business Performance Management Singapore. As of now, it is a non-commercial website, and information is shared for educational purposes. Please see licensing conditions and terms of use.

Sensitivity analysis is a fundamental concept in the effective use and implementation of quantitative decision models, whose purpose is to assess the stability of an optimal solution under changes in the parameters. (Dantzig)

Weighted sum model (Alternative Evaluation)

In AHP the preference Pi of alternative Ai is calculated using the following formula (weighted sum model):
(1)with Wj the weight of criterion Cj, and aijthe performance measure of alternative Aiwith respect to criterion Cj. Performance values are normalized.
(2)

As part of my current work about AHP scales, here an important finding for the balanced scale:

Salo and Hamalainen [1] pointed out that the integers from 1 to 9 yield local weights, which are not equally dispersed. Based on this observation, they proposed a balanced scale, where local weights are evenly dispersed over the weight range [0.1, 0.9]. They state that for a given set of priority vectors the corresponding ratios can be computed from the inverse relationship

r = w / (1 – w) (1a)

The priorities 0.1, 0.15, 0.2, … 0.8, 0.9 lead, for example, to the scale 1, 1.22, 1.5, 1.86, 2.33, 3.00, 4.00, 5.67 and 9.00. This scale can be computed by

wbal = 0.45 + 0.05 x (1b)

with x = 1 … 9 and

(1c)

c ( resp. 1/c) are the entry values in the decision matrix, and x the pairwise comparison judgment on the scale 1 to 9.

In fact, eq. 1a or its inverse are the special case forone selected pairwise comparison of two criteria. If we take into account the complete n x n decision matrix for n criteria, the resulting weights for one criterion, judged as x-times more important than all others, can be calculated as:

(2)

Eq. 2 simplifies to eq. 1a for n=2.

With eq. 2 we can formulate the general case for the balanced scale, resulting in evenly dispersed weights for n criteria and a judgment x with x from 1 to M:

This was a question in researchgate.net, and the answer of Prof. Saaty – the creator of the method – is of course: “The AHP is the only accurate and rigorous mathematical way known for the measurement on intangibles. It is not going to get old for a long time.“, with a lot of answers from others following.

When it comes to AHP, it seems the scientific world is still divided in opponents and advocates of the method.

I answered with the statistic of my website: BPMSG has more than 4000 users of the online software AHP-OS, 600 of them active users with 1000 projects and more than 3500 decision makers. My AHP excel template reached nearly 21 thousand downloads. It clearly shows that the method is not outdated.

As a reply Nolberto wrote:

“No, I don´t think that AHP is outdated, but the fact that over than 1000 projects have been developed using AHP does not mean that their results are correct (which is impossible to check), or that the method is sound (which is easily challenged)… “

Here my answer:

yes, I agree, the numbers only show that AHP is not outdated (which was the original question). They don’t show, whether the results are correct or incorrect, but they also do not show whether the users did or did not realise the method’s drawbacks and limitations.

For me, as a practitioner, AHP is one of the supporting tools in decision making. The intention of a tool is what it does. A hammer intends to strike, a lever intends to lift. It is what they are made for.

From my users feedback I sometimes get the impression that some of them expect a decision making support tool to make the decision for them, and this is not what it is made for.

In my practical applications AHP helped me and the teams a lot to gain a better insight into a decision problem, to separate important from less important criteria and to achieve a group consensus and agreement how to tackle a problem or proceed with a project. Probably, this could be achieved with other tools too, but as you say, AHP is simple, understandable and easy.

For sure, real world problems are complex. Therefore they have to be broken down and simplified, to be handled with the method, and I agree, over-simplification can be dangerous. On the other hand, what other approach than the break down of complex problems into digestable pieces is possible?

Finally, it’s not the tool producing the decision, but the humans behind it. They will be accountable for the decision, and it’s their responsibility to find the appropriate model of a decision problem and the right balance between rational and non-rational arguments and potential consequences of their decision.